J Austral Math Soc Ser A 51 pp426--435, 1991.

A Dual Approach to Embedding the Complement of Two Lines in a Finite Projective Plane

Lynn Margaret Batten

Abstract

Let S be a finite linear space on v ³ n² - n points and b = n² + n + 1 - m lines, m ³ 0, n ³ 1, such that at most m points are not on n + 1 lines. If m ³ 1, except if m = 1 and a unique point on n lines is on no line with two points, then S embeds uniquely in a projective plane of order n, or is one exceptional case if if n = 4. If m £ 1 and if v ³ n² - 2Ö(n + 3) + 6, the same conclusion holds, except possibly for the uniqueness.

1991 AMS Subject Classification: 05B05, 51E10

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Authors

Lynn Margaret Batten

Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2.